On the ascent of atomicity to monoid algebras

F Gotti, H Rabinovitz - Journal of Algebra, 2025 - Elsevier
A commutative cancellative monoid is atomic if every non-invertible element factors into
irreducibles (also called atoms), while an integral domain is atomic if its multiplicative …

On finitary power monoids of linearly orderable monoids

J Dani, F Gotti, L Hong, B Li, S Schlessinger - arxiv preprint arxiv …, 2025 - arxiv.org
A commutative monoid $ M $ is called a linearly orderable monoid if there exists a total order
on $ M $ that is compatible with the monoid operation. The finitary power monoid of a …

On primality and atomicity of numerical power monoids

A Aggarwal, F Gotti, S Lu - arxiv preprint arxiv:2412.05857, 2024 - arxiv.org
In the first part of this paper, we establish a variation of a recent result by Bienvenu and
Geroldinger on the (almost) non-existence of absolute irreducibles in (restricted) power …

On maximal common divisors in Puiseux monoids

E Liang, A Wang, L Zhong - arxiv preprint arxiv:2410.09251, 2024 - arxiv.org
Let $ M $ be a commutative monoid. An element $ d\in M $ is called a maximal common
divisor of a nonempty subset $ S $ of $ M $ if $ d $ is a common divisor of $ S $ in $ M $ and …

[PDF][PDF] Finitary Power Monoids: Atomicity, Divisibility, and Beyond

J Dani, L Hong, S Schlessinger - 2024 - math.mit.edu
Finitary Power Monoids: Atomicity, Divisibility, and Beyond Page 1 Finitary Power Monoids:
Atomicity, Divisibility, and Beyond Jiya Dani, Leo Hong, and Shimon Schlessinger MIT …